YTA. Hope that's clear enough for you, because it seems you can't fathom why your choice to be stingy about an extra $15 to add your nanny to the membership (because your wife should have been put down before the nanny) is offensive to your wife. Did you even consider that maybe your wife would like to go out with the family? Just because she has a stricter schedule and may be on call doesn't mean she wouldn't want to go out. And if you did go out with your family of 4, when presenting your membership to the employees, wouldn't your wife be blindsided by the fact that she is not part of the family of 4 on the membership and you couldn't be bothered to just spend and extra $15 to ensure no one was left out?

I would definitely be offended if my own husband left me out of a family membership so he could add the nanny, especially if he was too cheap to spend an extra $15 for me.